Question

Explain why 1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar

Answer 1

Hello,

There are only 2 solutions for $1.19

In cents:
119=1*25+9*10+0*5+4*1
119=3*25+4*10+0*5+4*1

Thus
120=119+1=(1*25+9*10+0*5+4*1) +1 =1*25+9*10+0*5+5*1
but 1*25+7*10+0*5+5*1=100

120=119+1=(3*25+4*10+0*5+4*1)+1=3*25+4*10+0*5+5*1
but 3*25+2*10+0*5+5*1=100

So there are no solution for $1.20